Signal Processing.pdf

DSP System Toolbox™ Getting Started Guide

R2016b

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The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 DSP System Toolbox™ Getting Started Guide © COPYRIGHT 2011–2016 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by, for, or through the federal government of the United States. By accepting delivery of the Program or Documentation, the government hereby agrees that this software or documentation qualifies as commercial computer software or commercial computer software documentation as such terms are used or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and conditions of this Agreement and only those rights specified in this Agreement, shall pertain to and govern the use, modification, reproduction, release, performance, display, and disclosure of the Program and Documentation by the federal government (or other entity acquiring for or through the federal government) and shall supersede any conflicting contractual terms or conditions. If this License fails to meet the government's needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to The MathWorks, Inc.

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Revision History

April 2011 September 2011 March 2012 September 2012 March 2013 September 2013 March 2014 October 2014 March 2015 September 2015 March 2016 September 2016

First printing Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only Online only

Revised for Version 8.0 (R2011a) Revised for Version 8.1 (R2011b) Revised for Version 8.2 (R2012a) Revised for Version 8.3 (R2012b) Revised for Version 8.4 (R2013a) Revised for Version 8.5 (R2013b) Revised for Version 8.6 (R2014a) Revised for Version 8.7 (R2014b) Revised for Version 9.0 (R2015a) Revised for Version 9.1 (R2015b) Revised for Version 9.2 (R2016a) Revised for Version 9.3 (R2016b)

Contents

1

Introduction DSP System Toolbox Product Description . . . . . . . . . . . . . . . Key Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-2 1-2

Configure Simulink Environment for Signal Processing Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Required Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-3 1-3 1-3 1-4

ARM Cortex-M and ARM Cortex-A Optimization . . . . . . . . . .

1-5

Configure the Simulink Environment for Signal Processing Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . About DSP Simulink Model Templates . . . . . . . . . . . . . . . . . Create Model Using the DSP System Toolbox Simulink Model Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DSP Simulink Model Templates . . . . . . . . . . . . . . . . . . . . . . See Also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1-6 1-6 1-6 1-7 1-13

Design a Filter with fdesign and Filter Builder Filter Design Process Overview . . . . . . . . . . . . . . . . . . . . . . .

2-2

Design a Filter Using fdesign . . . . . . . . . . . . . . . . . . . . . . . . .

2-3

Design a Filter Using Filter Builder . . . . . . . . . . . . . . . . . . . .

2-8

v

3

4

vi

Contents

Design Filters in Simulink Design and Implement a Filter . . . . . . . . . . . . . . . . . . . . . . . . Design a Digital Filter in Simulink . . . . . . . . . . . . . . . . . . . . Add a Digital Filter to Your Model . . . . . . . . . . . . . . . . . . . .

3-2 3-2 3-6

Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design an Adaptive Filter in Simulink . . . . . . . . . . . . . . . . Add an Adaptive Filter to Your Model . . . . . . . . . . . . . . . . . View the Coefficients of Your Adaptive Filter . . . . . . . . . . .

3-10 3-10 3-15 3-20

System Objects What Is a System Toolbox? . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-2

What Are System Objects? . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-3

System Objects vs. MATLAB Functions . . . . . . . . . . . . . . . . . System Objects vs. MATLAB Functions . . . . . . . . . . . . . . . . Process Audio Data Using Only MATLAB Functions Code . . Process Audio Data Using System Objects . . . . . . . . . . . . . .

4-5 4-5 4-5 4-6

System Design and Simulation in MATLAB . . . . . . . . . . . . . .

4-8

System Design and Simulation in Simulink . . . . . . . . . . . . . .

4-9

System Objects in MATLAB Code Generation . . . . . . . . . . . System Objects in Generated Code . . . . . . . . . . . . . . . . . . . System Objects in codegen . . . . . . . . . . . . . . . . . . . . . . . . . System Objects in the MATLAB Function Block . . . . . . . . . System Objects in the MATLAB System Block . . . . . . . . . . System Objects and MATLAB Compiler Software . . . . . . . .

4-10 4-10 4-15 4-15 4-16 4-16

System Objects Methods That Support Code Generation . . Code Generation Supported System Objects Methods . . . . . Simulation-Only System Objects Methods . . . . . . . . . . . . . .

4-17 4-17 4-17

System Objects in Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . System Objects in the MATLAB Function Block . . . . . . . . . System Objects in the MATLAB System Block . . . . . . . . . .

4-19 4-19 4-19

System Object Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What Are System Object Methods? . . . . . . . . . . . . . . . . . . . Running a System Object . . . . . . . . . . . . . . . . . . . . . . . . . . Common Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-20 4-20 4-20 4-21

System Design in MATLAB Using System Objects . . . . . . . . Predefined Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . Create Components for Your System . . . . . . . . . . . . . . . . . . Component Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configure Component Property Values . . . . . . . . . . . . . . . . Create and Configure Components at the Same Time . . . . . Connecting System Objects . . . . . . . . . . . . . . . . . . . . . . . . . Connect Components in a System . . . . . . . . . . . . . . . . . . . . Run Your System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reconfiguring Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Change a Tunable Property in Your System . . . . . . . . . . . .

4-23 4-23 4-23 4-24 4-24 4-25 4-25 4-25 4-26 4-26 4-27

System Design in Simulink Using System Objects . . . . . . . Define New Kinds of System Objects for Use in Simulink . . Test New System Objects in MATLAB . . . . . . . . . . . . . . . . Add System Objects to Your Simulink Model . . . . . . . . . . .

4-28 4-28 4-33 4-34

vii

1 Introduction • “DSP System Toolbox Product Description” on page 1-2 • “Configure Simulink Environment for Signal Processing Models” on page 1-3 • “ARM Cortex-M and ARM Cortex-A Optimization” on page 1-5 • “Configure the Simulink Environment for Signal Processing Models” on page 1-6

1

Introduction

DSP System Toolbox Product Description Design and simulate streaming signal processing systems DSP System Toolbox™ provides algorithms, apps, and scopes for designing, simulating, and analyzing signal processing systems in MATLAB® and Simulink®. You can model real-time DSP systems for communications, radar, audio, medical devices, IoT, and other applications. With DSP System Toolbox you can design and analyze FIR, IIR, multirate, multistage, and adaptive filters. You can stream signals from variables, data files, and network devices for system development and verification. The Time Scope, Spectrum Analyzer, and Logic Analyzer let you dynamically visualize and measure streaming signals. For desktop prototyping and deployment to embedded processors, including ARM® Cortex® architectures, the toolbox supports C/C++ code generation. It also supports bit-accurate fixed-point modeling and HDL code generation from filters, FFT, IFFT, and other algorithms. Algorithms are available as MATLAB functions, System objects, and Simulink blocks.

Key Features • Signal processing and linear algebra blocks for Simulink • Streaming signal processing in MATLAB • Single-rate, multirate, FIR, IIR, and adaptive filter design • Time Scope, Spectrum Analyzer, and Logic Analyzer for visualizing and measuring streaming signals • Fixed-point modeling and simulation of signal processing algorithms • Support for C and C++ code generation • Support for HDL code generation

1-2

Configure Simulink Environment for Signal Processing Models

Configure Simulink Environment for Signal Processing Models In this section... “Installation” on page 1-3 “Required Products” on page 1-3 “Related Products” on page 1-4

Installation Before you begin working, you need to install the product on your computer. Installing the DSP System Toolbox Software The DSP System Toolbox software follows the same installation procedure as the MATLAB toolboxes. Installing Online Documentation Installing the documentation is part of the installation process: • Installation from a DVD — Start the MathWorks® installer. When prompted, select the Product check boxes for the products you want to install. The documentation is installed along with the products. • Installation from a Web download — If you update the DSP System Toolbox software using a Web download and you want to view the documentation with the MATLAB Help browser, you must install the documentation on your hard drive. Download the files from the Web. Then, start the installer, and select the Product check boxes for the products you want to install. The documentation is installed along with the products.

Required Products The DSP System Toolbox product is part of a family of MathWorks products. You need to install several products to use the toolbox. For more information about the required products, see the MathWorks Web site, at http://www.mathworks.com/products/ dsp-system/requirements.html. 1-3

1

Introduction

Related Products MathWorks provides several products that are relevant to the kinds of tasks you can perform with DSP System Toolbox software. For more information about any of these products, see either • The online documentation for that product if it is installed on your system • The MathWorks Web site, at http://www.mathworks.com/products/dspsystem/related.html.

1-4

ARM Cortex-M and ARM Cortex-A Optimization

ARM Cortex-M and ARM Cortex-A Optimization The DSP System Toolbox supports optimized C code generation for popular algorithms like FIR filtering and FFT on ARM Cortex-M and ARM Cortex-A processors. You can generate C code that can be linked with the CMSIS library or calls the Ne10 library functions and compiled to provide optimized executables to run on ARM Cortex-M or ARM Cortex-A processors. To use the DSP System Toolbox support packages for ARM Cortex-M and ARM Cortex-A processors, you must have the following products in addition to the DSP System Toolbox: Simulink, Simulink Coder™ , Embedded Coder®, and MATLAB Coder. To obtain more information and download the DSP System Toolbox support packages for the ARM Cortex processors, see http://www.mathworks.com/hardware-support/ index.html.

1-5

1

Introduction

Configure the Simulink Environment for Signal Processing Models In this section... “About DSP Simulink Model Templates” on page 1-6 “Create Model Using the DSP System Toolbox Simulink Model Template” on page 1-6 “DSP Simulink Model Templates” on page 1-7 “See Also” on page 1-13

About DSP Simulink Model Templates The DSP Simulink model templates let you automatically configure the Simulink environment with the recommended settings for digital signal processing modeling. DSP Simulink model templates enable reuse of settings, including configuration parameters. You can create models from templates that use best practices and take advantage of previous solutions to common problems. Instead of the default canvas of a new model, select a template model to help you get started. For more information on Simulink model templates, see “Create a Model” in the Simulink documentation.

Create Model Using the DSP System Toolbox Simulink Model Template To create a new blank model and open the library browser:

1-6

1

On the MATLAB Home tab, click Simulink.

2

Click on DSP System to create an empty model with settings suitable for use with DSP System Toolbox. The new model opens. To access the library browser, click the Library Browser button on the model toolbar.

Configure the Simulink Environment for Signal Processing Models

The new model using the template settings and contents appears in the Simulink Editor. The model is only in memory until you save it.

DSP Simulink Model Templates When you create a model by choosing one of the DSP Simulink model templates, the model is configured to use the settings recommended for DSP System Toolbox. Some of these settings are: Configuration Parameter

Setting

SingleTaskRateTransMsg

error

multiTaskRateTransMsg

error

Solver

fixedstepdiscrete

EnableMultiTasking

Off

StartTime

0.0

1-7

1

Introduction

Configuration Parameter

Setting

StopTime

inf

FixedStep

auto

SaveTime

off

SaveOutput

off

AlgebraicLoopMsg

error

SignalLogging

off

FrameProcessingCompatibilityMsg

error

The DSP Simulink model templates are: • “DSP System Template” on page 1-8 • “Basic Filter Template” on page 1-9 • “ARM Cortex-A Model Template” on page 1-10 • “ARM Cortex-M Model Template” on page 1-11 • “Mixed-Signal System Template” on page 1-12 DSP System Template Click on DSP System to create a blank model configured with settings recommended for DSP System Toolbox.

1-8

Configure the Simulink Environment for Signal Processing Models

Basic Filter Template Click on Basic Filter to create a basic filtering model configured with settings recommended for DSP System Toolbox. This model implements a low pass filter and enables you to compare the filtered signal with the original signal. The model acts as a starting point for modeling filtering algorithms in Simulink using DSP System Toolbox.

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1

Introduction

ARM Cortex-A Model Template Click the ARM Cortex-A Model to create a basic model for code replacement with the Ne10 library, which is optimized for ARM Cortex-A Processors. This model is configured with settings recommended for DSP System Toolbox and ARM Cortex-A processors.

1-10

Configure the Simulink Environment for Signal Processing Models

ARM Cortex-M Model Template Click the ARM Cortex-M Model to create a basic model for code replacement with the CMSIS library, which is optimized for ARM Cortex-M processors. This model is configured with settings recommended for DSP System Toolbox and ARM Cortex-M processors.

1-11

1

Introduction

Mixed-Signal System Template Click the Mixed-Signal System template to create a basic A/D converter model configured with settings recommended for DSP System Toolbox and mixed-signal systems. This model performs A/D conversion by implementing an analog antialiasing filter followed by a zero-order hold circuit. The model acts as a starting point for modeling mixed-signal systems in Simulink using DSP System Toolbox. All discrete-time signals are colored in red to indicate the fastest sample rate. Continuous-time signals are colored in black. For additional sample time options, from the Display menu, select Sample Time.

1-12

Configure the Simulink Environment for Signal Processing Models

See Also • “Filter Frames of a Noisy Sine Wave Signal in Simulink” 1-13

2 Design a Filter with fdesign and Filter Builder • “Filter Design Process Overview” on page 2-2 • “Design a Filter Using fdesign” on page 2-3 • “Design a Filter Using Filter Builder” on page 2-8

2

Design a Filter with fdesign and Filter Builder

Filter Design Process Overview Note: You must have the Signal Processing Toolbox installed to use fdesign and filterBuilder. Advanced capabilities are available if your installation additionally includes the DSP System Toolbox license. You can verify the presence of both toolboxes by typing ver at the command prompt. Filter design through user-defined specifications is the core of the fdesign approach. This specification-centric approach places less emphasis on the choice of specific filter algorithms, and more emphasis on performance during the design a good working filter. For example, you can take a given set of design parameters for the filter, such as a stopband frequency, a passband frequency, and a stopband attenuation, and— using these parameters— design a specification object for the filter. You can then implement the filter using this specification object. Using this approach, it is also possible to compare different algorithms as applied to a set of specifications. There are two distinct objects involved in filter design: • Specification Object — Captures the required design parameters of a filter • Implementation Object — Describes the designed filter; includes the array of coefficients and the filter structure The distinction between these two objects is at the core of the filter design methodology. The basic attributes of each of these objects are outlined in the following table. Specification Object

Implementation Object

High-level specification

Filter coefficients

Algorithmic properties

Filter structure

You can run the code in the following examples from the Help browser (select the code, right-click the selection, and choose Evaluate Selection from the context menu), or you can enter the code on the MATLAB command line. Before you begin this example, start MATLAB and verify that you have installed the Signal Processing Toolbox software. If you wish to access the full functionality of fdesign and filterBuilder, you should additionally obtain the DSP System Toolbox software. You can verify the presence of these products by typing ver at the command prompt.

2-2

Design a Filter Using fdesign

Design a Filter Using fdesign Use the following two steps to design a simple filter. 1

Create a filter specification object.

2

Design your filter.

Design a Filter in Two Steps Assume that you want to design a bandpass filter. Typically a bandpass filter is defined as shown in the following figure.

In this example, a sampling frequency of Fs = 48 kHz is used. This bandpass filter has the following specifications, specified here using MATLAB code: A_stop1 = 60; % Attenuation in the first stopband = 60 dB F_stop1 = 8400; % Edge of the stopband = 8400 Hz F_pass1 = 10800; % Edge of the passband = 10800 Hz F_pass2 = 15600; % Closing edge of the passband = 15600 Hz F_stop2 = 18000; % Edge of the second stopband = 18000 Hz A_stop2 = 60; % Attenuation in the second stopband = 60 dB A_pass = 1; % Amount of ripple allowed in the passband = 1 dB

In the following two steps, these specifications are passed to the fdesign.bandpass method as parameters. Step 1 2-3

2

Design a Filter with fdesign and Filter Builder

To create a filter specification object, evaluate the following code at the MATLAB prompt: d = fdesign.bandpass

Now, pass the filter specifications that correspond to the default Specification — fst1,fp1,fp2,fst2,ast1,ap,ast2. This example adds fs as the final input argument to specify the sampling frequency of 48 kHz. >> BandPassSpecObj = ... fdesign.bandpass('Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2', ... F_stop1, F_pass1, F_pass2, F_stop2, A_stop1, A_pass, ... A_stop2, 48000)

Note: The order of the filter is not specified, allowing a degree of freedom for the algorithm design in order to achieve the specification. The design will be a minimum order design. The specification parameters, such as Fstop1, are all given default values when none are provided. You can change the values of the specification parameters after the filter specification object has been created. For example, if there are two values that need to be changed, Fpass2 and Fstop2, use the set command, which takes the object first, and then the parameter value pairs. Evaluate the following code at the MATLAB prompt: >> set(BandPassSpecObj, 'Fpass2', 15800, 'Fstop2', 18400)

BandPassSpecObj is the new filter specification object which contains all the required design parameters, including the filter type. You may also change parameter values in filter specification objects by accessing them as if they were elements in a struct array. >> BandPassSpecObj.Fpass2=15800;

Step 2 Design the filter by using the design command. You can access the design methods available for you specification object by calling the designmethods function. For example, in this case, you can execute the command >> designmethods(BandPassSpecObj)

2-4

Design a Filter Using fdesign

Design Methods for class fdesign.bandpass (Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2):

butter cheby1 cheby2 ellip equiripple kaiserwin

After choosing a design method use, you can evaluate the following at the MATLAB prompt (this example assumes you've chosen 'equiripple'): >> BandPassFilt = design(BandPassSpecObj, 'equiripple') BandPassFilt = FilterStructure: Arithmetic: Numerator: PersistentMemory:

'Direct-Form FIR' 'double' [1x44 double] false

If you have the DSP System Toolbox installed, you can also design your filter with a filter System object™. To create a filter System object with the same specification object BandPassSpecObj, you can execute the commands >> designmethods(BandPassSpecObj,... 'SystemObject',true)

Design Methods that support System objects for class fdesign.bandpass (Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2):

butter cheby1 cheby2 ellip equiripple kaiserwin

2-5

2

Design a Filter with fdesign and Filter Builder

>> BandPassFiltSysObj = design(BandPassSpecObj,... 'equiripple','SystemObject',true)

System: dsp.FIRFilter Properties: Structure: NumeratorSource: Numerator: InitialConditions: FrameBasedProcessing:

'Direct form' 'Property' [1x44 double] 0 true

Show fixed-point properties

Available design methods and design options for filter System objects are not necessarily the same as those for filter objects. Note: If you do not specify a design method, a default method will be used. For example, you can execute the command >> BandPassFilt = design(BandPassSpecObj) BandPassFilt = FilterStructure: Arithmetic: Numerator: PersistentMemory:

'Direct-Form FIR' 'double' [1x44 double] false

and a design method will be selected automatically. To check your work, you can plot the filter magnitude response using the Filter Visualization tool. Verify that all the design parameters are met: >> fvtool(BandPassFilt) %plot the filter magnitude response

If you have the DSP System Toolbox installed, the Filter Visualization tool produces the following figure with the dashed red lines indicating the transition bands and unity gain (0 in dB) over the passband.

2-6

Design a Filter Using fdesign

2-7

2

Design a Filter with fdesign and Filter Builder

Design a Filter Using Filter Builder Filter Builder presents the option of designing a filter using a GUI dialog box as opposed to the command line instructions. You can use Filter Builder to design the same bandpass filter designed in the previous section, “Design a Filter Using fdesign” on page 2-3 Design a Simple Filter in Filter Builder To design the filter using the Filter Builder GUI: 1

Type the following at the MATLAB prompt: filterBuilder

2

Select Bandpass filter response from the list in the dialog box, and hit the OK button.

3

Enter the correct frequencies for Fpass2 and Fstop2, then click OK. Here the specification uses normalized frequency, so that the passband and stopband edges are expressed as a fraction of the Nyquist frequency (in this case, 48/2 kHz). The following message appears at the MATLAB prompt: The variable 'Hbp' has been exported to the command window.

If you display the Workspace tab, you see the object Hbp has been placed on your workspace. 4

To check your work, plot the filter magnitude response using the Filter Visualization tool. Verify that all the design parameters are met: fvtool(Hbp) %plot the filter magnitude response

2-8

Design a Filter Using Filter Builder

Note that the dashed red lines on the preceding figure will only appear if you are using the DSP System Toolbox software.

2-9

3 Design Filters in Simulink • “Design and Implement a Filter” on page 3-2 • “Adaptive Filters” on page 3-10

3

Design Filters in Simulink

Design and Implement a Filter In this section... “Design a Digital Filter in Simulink” on page 3-2 “Add a Digital Filter to Your Model” on page 3-6

Design a Digital Filter in Simulink You can design lowpass, highpass, bandpass, and bandstop filters using either the Digital Filter Design block or the Filter Realization Wizard. These blocks are capable of calculating filter coefficients for various filter structures. In this section, you use the Digital Filter Design block to convert white noise to low frequency noise so you can simulate its effect on your system. As a practical application, suppose a pilot is speaking into a microphone within the cockpit of an airplane. The noise of the wind passing over the fuselage is also reaching the microphone. A sensor is measuring the noise of the wind on the outside of the plane. You want to estimate the wind noise inside the cockpit and subtract it from the input to the microphone so that only the pilot's voice is transmitted. In this chapter, you first learn how to model the low frequency noise that is reaching the microphone. Later, you learn how to remove this noise so that only the pilot's voice is heard. In this topic, you use a Digital Filter Design block to create low frequency noise, which models the wind noise inside the cockpit: 1

Open the model by typing ex_gstut3

at the MATLAB command prompt. This model contains a Scope block that displays the original sine wave and the sine wave with white noise added.

3-2

Design and Implement a Filter

2

Open the DSP System Toolbox library by typing dsplib at the MATLAB command prompt.

3

Convert white noise to low frequency noise by introducing a Digital Filter Design block into your model. In the airplane scenario, the air passing over the fuselage creates white noise that is measured by a sensor. The Random Source block models this noise. The fuselage of the airplane converts this white noise to low frequency noise, a type of colored noise, which is heard inside the cockpit. This noise contains only certain frequencies and is more difficult to eliminate. In this example, you model the low frequency noise using a Digital Filter Design block. This block uses the functionality of the Filter Design and Analysis Tool (FDATool) to design a filter. Double-click the Filtering library, and then double-click the Filter Implementations sublibrary. Click-and-drag the Digital Filter Design block into your model.

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3

Design Filters in Simulink

4

Set the Digital Filter Design block parameters to design a lowpass filter and create low frequency noise. Open the block parameters dialog box by double-clicking the block. Set the parameters as follows: • Response Type = Lowpass • Design Method = FIR and, from the list, choose Window • Filter Order = Specify order and enter 31 • Scale Passband — Cleared • Window = Hamming • Units = Normalized (0 to 1) • wc = 0.5

3-4

Design and Implement a Filter

Based on these parameters, the Digital Filter Design block designs a lowpass FIR filter with 32 coefficients and a cutoff frequency of 0.5. The block multiplies the timedomain response of your filter by a 32 sample Hamming window. 5

Click Design Filter at the bottom center of the dialog box to view the magnitude response of your filter in the Magnitude Response pane. The Digital Filter Design dialog box should now look similar to the following figure.

You have now designed a digital lowpass filter using the Digital Filter Design block. You can experiment with the Digital Filter Design block in order to design a filter of your own. For more information on the block functionality, see the Digital Filter Design

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3

Design Filters in Simulink

block reference page. For more information on the Filter Design and Analysis Tool, see “Filter Designer” in the Signal Processing Toolbox documentation.

Add a Digital Filter to Your Model In this topic, you add the lowpass filter you designed in “Design a Digital Filter in Simulink” on page 3-2 to your block diagram. Use this filter, which converts white noise to colored noise, to simulate the low frequency wind noise inside the cockpit: 1

If the model you created in “Design a Digital Filter in Simulink” on page 3-2 is not open on your desktop, you can open an equivalent model by typing ex_gstut4

at the MATLAB command prompt.

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Design and Implement a Filter

2

Incorporate the Digital Filter Design block into your block diagram by placing it between the Random Source block and the Sum block.

3-7

3

Design Filters in Simulink

3

3-8

Run your model and view the results in the Scope window. This window shows the original input signal and the signal with low frequency noise added to it.

Design and Implement a Filter

You have now built a digital filter and used it to model the presence of colored noise in your signal. This is analogous to modeling the low frequency noise reaching the microphone in the cockpit of the aircraft. Now that you have added noise to your system, you can experiment with methods to eliminate it.

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3

Design Filters in Simulink

Adaptive Filters In this section... “Design an Adaptive Filter in Simulink” on page 3-10 “Add an Adaptive Filter to Your Model” on page 3-15 “View the Coefficients of Your Adaptive Filter” on page 3-20

Design an Adaptive Filter in Simulink Adaptive filters track the dynamic nature of a system and allow you to eliminate timevarying signals. The DSP System Toolbox libraries contain blocks that implement leastmean-square (LMS), Block LMS, Fast Block LMS, and recursive least squares (RLS) adaptive filter algorithms. These filters minimize the difference between the output signal and the desired signal by altering their filter coefficients. Over time, the adaptive filter's output signal more closely approximates the signal you want to reproduce. In this topic, you design an LMS adaptive filter to remove the low frequency noise in your signal: 1

If the model you created in “Add a Digital Filter to Your Model” on page 3-6 is not open on your desktop, you can open an equivalent model by typing ex_gstut5

at the MATLAB command prompt.

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Adaptive Filters

2

Open the DSP System Toolbox library by typing dsplib at the MATLAB command prompt.

3

Remove the low frequency noise from your signal by adding an LMS Filter block to your system. In the airplane scenario, this is equivalent to subtracting the wind noise inside the cockpit from the input to the microphone. Double-click the Filtering sublibrary, and then double-click the Adaptive Filters library. Add the LMS Filter block into your model.

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Set the LMS Filter block parameters to model the output of the Digital Filter Design block. Open its dialog box by double-clicking the block. Set the block parameters as follows:

Adaptive Filters

• Algorithm = Normalized LMS • Filter length = 32 • Specify step size via = Dialog • Step size (mu) = 0.1 • Leakage factor (0 to 1) = 1.0 • Initial value of filter weights = 0 • Clear the Adapt port check box. • Reset port = None • Select the Output filter weights check box. The LMS Filter dialog box should now look like the following figure:

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5

Click Apply.

Based on these parameters, the LMS Filter block computes the filter weights using the normalized LMS equations. The filter order you specified is the same as the filter order of the Digital Filter Design block. The Step size (mu) parameter defines the granularity of the filter update steps. Because you set the Leakage factor (0 to 1) parameter to 1.0, the current filter coefficient values depend on the filter's initial conditions and all of the previous input values. The initial value of the filter weights (coefficients) is zero. Since you selected the Output filter weights check box, the Wts port appears on the block. The block outputs the filter weights from this port. Now that you have set the block parameters of the LMS Filter block, you can incorporate this block into your block diagram.

Add an Adaptive Filter to Your Model In this topic, you recover your original sinusoidal signal by incorporating the adaptive filter you designed in “Design an Adaptive Filter in Simulink” on page 3-10 into your system. In the aircraft scenario, the adaptive filter models the low frequency noise heard inside the cockpit. As a result, you can remove the noise so that the pilot's voice is the only input to the microphone: 1

If the model you created in “Design an Adaptive Filter in Simulink” on page 3-10 is not open on your desktop, you can open an equivalent model by typing ex_gstut6

at the MATLAB command prompt.

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Design Filters in Simulink

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2

Add a Sum block to your model to subtract the output of the adaptive filter from the sinusoidal signal with low frequency noise. From the Simulink Math Operations library, drag a Sum block into your model. Open the Sum dialog box by doubleclicking this block. Change the List of signs parameter to |+- and then click OK.

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Incorporate the LMS Filter block into your system. a

Connect the output of the Random Source block to the Input port of the LMS Filter block. In the aircraft scenario, the random noise is the white noise measured by the sensor on the outside of the airplane. The LMS Filter block models the effect of the airplane's fuselage on the noise.

b

Connect the output of the Digital Filter Design block to the Desired port on the LMS Filter block. This is the signal you want the LMS block to reproduce.

c

Connect the output of the LMS Filter block to the negative port of the Sum block you added in step 2.

Adaptive Filters

d

Connect the output of the first Sum block to the positive port of the second Sum block. Your model should now look similar to the following figure.

The positive input to the second Sum block is the sum of the input signal and the low frequency noise, s(n) + y. The negative input to the second Sum block is the LMS Filter block's best estimation of the low frequency noise, y'. When you subtract the two signals, you are left with an approximation of the input signal.

s( n) approx = s(n) + y - y’ 3-17

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In this equation: • s(n) is the input signal •

s( n) approx is the approximation of the input signal

• y is the noise created by the Random Source block and the Digital Filter Design block • y' is the LMS Filter block's approximation of the noise Because the LMS Filter block can only approximate the noise, there is still a difference between the input signal and the approximation of the input signal. In subsequent steps, you set up the Scope block so you can compare the original sinusoidal signal with its approximation.

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Add two additional inputs and axes to the Scope block. Open the Scope dialog box by double-clicking the Scope block. Click the Parameters button. For the Number of axes parameter, enter 4. Close the dialog box by clicking OK.

5

Label the new Scope axes. In the Scope window, right-click on the third axes and select Axes properties. The Scope properties: axis 3 dialog box opens. In the Title box, enter Approximation of Input Signal. Close the dialog box by clicking OK. Repeat this procedure for the fourth axes and label it Error.

6

Connect the output of the second Sum block to the third port of the Scope block.

7

Connect the output of the Error port on the LMS Filter block to the fourth port of the Scope block. Your model should now look similar to the following figure.

Adaptive Filters

In this example, the output of the Error port is the difference between the LMS filter's desired signal and its output signal. Because the error is never zero, the filter continues to modify the filter coefficients in order to better approximate the low frequency noise. The better the approximation, the more low frequency noise that can be removed from the sinusoidal signal. In the next topic, “View the Coefficients of Your Adaptive Filter” on page 3-20, you learn how to view the coefficients of your adaptive filter as they change with time.

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View the Coefficients of Your Adaptive Filter The coefficients of an adaptive filter change with time in accordance with a chosen algorithm. Once the algorithm optimizes the filter's performance, these filter coefficients reach their steady-state values. You can view the variation of your coefficients, while the simulation is running, to see them settle to their steady-state values. Then, you can determine whether you can implement these values in your actual system: 1

If the model you created in “Add an Adaptive Filter to Your Model” on page 3-15 is not open on your desktop, you can open an equivalent model by typing ex_gstut7

at the MATLAB command prompt. Note that the Wts port of the adaptive filter, which outputs the filter weights, still needs to be connected.

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2

Open the DSP System Toolbox library by typing dsplib at the MATLAB command prompt.

3

View the filter coefficients using a Vector Scope block from the Sinks library.

4

Open the Vector Scope dialog box by double-clicking the block. Set the block parameters as follows: a

Click the Scope Properties tab. • Input domain = Time

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• Time display span (number of frames) = 1 b

Click the Display Properties tab. • Select the following check boxes: • Show grid • Frame number • Compact display • Open scope at start of simulation

c

Click the Axis Properties tab. • Minimum Y-limit = -0.2 • Maximum Y-limit = 0.6 • Y-axis label = Filter Weights

d

Click the Line Properties tab. • Line visibilities = on • Line style = : • Line markers = . • Line colors = [0 0 1]

e 5

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Click OK.

Connect the Wts port of the LMS Filter block to the Vector Scope block.

Adaptive Filters

6

Set the configuration parameters: a

Open the Configuration Parameters dialog box by selecting Model Configuration Parameters from the Simulation menu, and navigate to the Solver pane.

b

Enter inf for the Stop time parameter.

c

Choose Fixed-step from the Type list.

d

Choose Discrete (no continuous states) from the Solver list.

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We recommend these configuration parameters for models that contain DSP System Toolbox blocks. Because these blocks calculate values directly rather than solving differential equations, you must configure the Simulink Solver to behave like a scheduler. The Solver, while in scheduler mode, uses a block's sample time to determine when the code behind each block is executed. For example, the sample time of the Sine Wave and Random Source blocks in this model is 0.05. The Solver executes the code behind these blocks, and every other block with this sample time, once every 0.05 second. Note: When working with models that contain DSP System Toolbox blocks, use source blocks that enable you to specify their sample time. If your source block does not have a Sample time parameter, you must add a Zero-Order Hold block in your model and use it to specify the sample time. For more information, see “ContinuousTime Source Blocks” in the DSP System Toolbox User's Guide. The exception to this rule is the Constant block, which can have a constant sample time. When it does, Simulink executes this block and records the constant value once at the start of the simulation and any time you tune a parameter. This allows for faster simulations and more compact generated code.

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Close the dialog box by clicking OK.

8

Open the Scope window by double-clicking the Scope block.

9

Run your model and view the behavior of your filter coefficients in the Vector Scope window, which opens automatically when your simulation starts. Over time, you see the filter coefficients change and approach their steady-state values, shown below.

Adaptive Filters

You can simultaneously view the behavior of the system in the Scope window. Over time, you see the error decrease and the approximation of the input signal more closely match the original sinusoidal input signal.

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You have now created a model capable of adaptive noise cancellation. So far, you have learned how to design a lowpass filter using the Digital Filter Design block. You also learned how to create an adaptive filter using the LMS Filter block. The DSP System Toolbox product has other blocks capable of designing and implementing digital and adaptive filters. For more information on the filtering capabilities of this product, see “Filter Design” and “Filter Analysis”. Because all blocks in this model have the same sample time, this model is single rate and Simulink ran it in SingleTasking solver mode. If the blocks in your model have different sample times, your model is multirate and Simulink might run it in MultiTasking solver mode. For more information on solver modes, see “Recommended Settings for Discrete-Time Simulations” in the DSP System Toolbox User's Guide. To learn how to generate code from your model using the Simulink Coder product, see the “C Code Generation from Simulink” section.

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4 System Objects • “What Is a System Toolbox?” on page 4-2 • “What Are System Objects?” on page 4-3 • “System Objects vs. MATLAB Functions” on page 4-5 • “System Design and Simulation in MATLAB” on page 4-8 • “System Design and Simulation in Simulink” on page 4-9 • “System Objects in MATLAB Code Generation” on page 4-10 • “System Objects Methods That Support Code Generation” on page 4-17 • “System Objects in Simulink” on page 4-19 • “System Object Methods” on page 4-20 • “System Design in MATLAB Using System Objects” on page 4-23 • “System Design in Simulink Using System Objects” on page 4-28

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What Is a System Toolbox? System Toolbox products provide algorithms and tools for designing, simulating, and deploying dynamic systems in MATLAB and Simulink. These toolboxes contain MATLAB functions, System objects, and Simulink blocks that deliver the same design and verification capabilities across MATLAB and Simulink, enabling more effective collaboration among system designers. Available System Toolbox products include: • DSP System Toolbox • Communications System Toolbox™ • Computer Vision System Toolbox™ • Phased Array System Toolbox™ System Toolboxes support floating-point and fixed-point streaming data simulation for both sample- and frame-based data. They provide a programming environment for defining and executing code for various aspects of a system, such as initialization and reset. System Toolboxes also support code generation for a range of system development tasks and workflows, such as: • Rapid development of reusable IP and test benches • Sharing of component libraries and systems models across teams • Large system simulation • C-code generation for embedded processors • Finite wordlength effects modeling and optimization • Ability to prototype and test on real-time hardware

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What Are System Objects?

What Are System Objects? A System object is a specialized kind of MATLAB object. System Toolboxes include System objects and most System Toolboxes also have MATLAB functions and Simulink blocks. System objects are designed specifically for implementing and simulating dynamic systems with inputs that change over time. Many signal processing, communications, and controls systems are dynamic. In a dynamic system, the values of the output signals depend on both the instantaneous values of the input signals and on the past behavior of the system. System objects use internal states to store that past behavior, which is used in the next computational step. As a result, System objects are optimized for iterative computations that process large streams of data in segments, such as video and audio processing systems. This ability to process streaming data provides the advantage of not having to hold large amounts of data in memory. Use of streaming data also allows you to use simplified programs that use loops efficiently. For example, you could use System objects in a system that reads data from a file, filters that data and then writes the filtered output to another file. Typically, a specified amount of data is passed to the filter in each loop iteration. The file reader object uses a state to keep track of where in the file to begin the next data read. Likewise, the file writer object keeps tracks of where it last wrote data to the output file so that data is not overwritten. The filter object maintains its own internal states to ensure that the filtering is performed correctly. This diagram represents a single loop of the system.

These advantages make System objects particularly well suited for processing streaming data Many System objects support: • Fixed-point arithmetic (requires a Fixed-Point Designer™ license) • C code generation (requires a MATLAB Coder or Simulink Coder license) • HDL code generation (requires an HDL Coder™ license) • Executable files or shared libraries generation (requires a MATLAB Compiler™ license) 4-3

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Note: Check your product documentation to confirm fixed-point, code generation, and MATLAB Compiler support for the specific System objects you want to use. System objects use a minimum of two commands to process data—a constructor to create the object (such as, fft256 = dsp.FFT) and a function call (such as, fft256(x)) to run data through the object. This separation of declaration from execution lets you create multiple, persistent, reusable objects, each with different settings. Using this approach avoids repeated input validation and verification, allows for easy use within a programming loop, and improves overall performance. In contrast, MATLAB functions must validate parameters every time you call the function. In addition to the System objects provided with System Toolboxes, you can also create your own System objects. See “Define System Objects”.

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System Objects vs. MATLAB Functions

System Objects vs. MATLAB Functions In this section... “System Objects vs. MATLAB Functions” on page 4-5 “Process Audio Data Using Only MATLAB Functions Code” on page 4-5 “Process Audio Data Using System Objects” on page 4-6

System Objects vs. MATLAB Functions Many System objects have MATLAB function counterparts. For simple, one-time computations use MATLAB functions. However, if you need to design and simulate a system with many components, use System objects. Using System objects is also appropriate if your computations require managing internal states, have inputs that change over time or process large streams of data. Building a dynamic system with different execution phases and internal states using only MATLAB functions would require complex programming. You would need code to initialize the system, validate data, manage internal states, and reset and terminate the system. System objects perform many of these managerial operations automatically during execution. By combining System objects in a program with other MATLAB functions, you can streamline your code and improve efficiency.

Process Audio Data Using Only MATLAB Functions Code This example shows how to write MATLAB® function-only code for reading audio data. The code reads audio data from a file, filters it, and then plays the filtered audio data. The audio data is read in frames. This code produces the same result as the System objects code in the next example, allowing you to compare approaches. Locate source audio file. fname = 'speech_dft_8kHz.wav';

Obtain the total number of samples and the sampling rate from the source file. audioInfo = audioinfo(fname); maxSamples = audioInfo.TotalSamples; fs = audioInfo.SampleRate;

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Define the filter to use. b = fir1(160,.15);

Initialize the filter states. z = zeros(1,numel(b)-1);

Define the amount of audio data to process at one time, and initialize the while loop index. frameSize = 1024; nIdx = 1;

Define the while loop to process the audio data in processloop. type processloop

while nIdx System Object > Simulink Extension menu option to open a template. This template includes customizations of the System object for use in the Simulink MATLAB System block. You edit the template file, using it as guideline, to create your own System object. On the first line of the class definition file, specify the name of your System object and subclass from both matlab.System and matlab.system.mixin.CustomIcon. The matlab.System base class enables you to use all the basic System object methods and specify the block input and output names, title, and property groups. The CustomIcon mixin class enables the method that lets you specify the block icon. 4-28

System Design in Simulink Using System Objects

Add the appropriate basic System object methods to set up, reset, set the number of inputs and outputs, and run your algorithm. See the reference pages for each method and the full class definition file below for the implementation of each of these methods. • Use the setupImpl method to perform one-time calculations and initialize variables. • Use the stepImpl method to implement the block’s algorithm. • Use the resetImpl method to reset the state properties or DiscreteState properties.

• Use the getNumInputsImpl and getNumOutputsImpl methods to specify the number of inputs and outputs, respectively. Add the appropriate CustomIcon methods to define the appearance of the MATLAB System block in Simulink. See the reference pages for each method and the full class definition file below for the implementation of each of these methods. • Use the getHeaderImpl method to specify the title and description to display on the block dialog. • Use the getPropertyGroupsImpl method to specify groups of properties to display on the block dialog. • Use the getIconImpl method to specify the text to display on the block icon.

• Use the getInputNamesImpl and getOutputNamesImpl methods to specify the labels to display for the block input and output ports. The full class definition file for the least mean squares filter is: classdef lmsSysObj < matlab.System &... matlab.system.mixin.CustomIcon % lmsSysObj Least mean squares (LMS) adaptive filtering. % #codegen properties % Mu Step size Mu = 0.005; end properties (Nontunable) % Weights Filter weights Weights = 0; % N Number of filter weights N = 32; end

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properties (DiscreteState) X; H; end methods (Access = protected) function setupImpl(obj) obj.X = zeros(obj.N,1); obj.H = zeros(obj.N,1); end function [y, e_norm] = stepImpl(obj,d,u) tmp = obj.X(1:obj.N-1); obj.X(2:obj.N,1) = tmp; obj.X(1,1) = u; y = obj.X'*obj.H; e = d-y; obj.H = obj.H + obj.Mu*e*obj.X; e_norm = norm(obj.Weights'-obj.H); end function resetImpl(obj) obj.X = zeros(obj.N,1); obj.H = zeros(obj.N,1); end end % Block icon and dialog customizations methods (Static, Access = protected) function header = getHeaderImpl header = matlab.system.display.Header(... 'lmsSysObj', ... 'Title', 'LMS Adaptive Filter'); end function groups = getPropertyGroupsImpl upperGroup = matlab.system.display.SectionGroup(... 'Title','General',... 'PropertyList',{'Mu'}); lowerGroup = matlab.system.display.SectionGroup(... 'Title','Coefficients', ... 'PropertyList',{'Weights','N'});

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System Design in Simulink Using System Objects

groups = [upperGroup,lowerGroup]; end end methods (Access = protected) function icon = getIconImpl(~) icon = sprintf('LMS Adaptive\nFilter'); end function [in1name, in2name] = getInputNamesImpl(~) in1name = 'Desired'; in2name = 'Actual'; end function [out1name, out2name] = getOutputNamesImpl(~) out1name = 'Output'; out2name = 'EstError'; end end end

Define System Object with Nondirect Feedthrough This example shows how to create a System object for use in Simulink. The example performs system identification using a least mean squares (LMS) adaptive filter and uses feedback loops. This example shows how to create a class definition text file to define your System object. The code in this example creates an integer delay and includes feedback loops, and customizations to the block icon. For information on feedback loops, see “Use System Objects in Feedback Loops”. This example implements a System object that you can use for nondirect feedthrough. It is similar to the System Identification Using MATLAB System Blocks Simulink example. On the first line of the class definition file, subclass from matlab.System and matlab.system.mixin.CustomIcon. The matlab.System base class enables you to use all the basic System object methods and specify the block input and output names, title, and property groups. The CustomIcon mixin class enables the method that lets you specify the block icon. The Nondirect mixin enables the methods that let you specify how the block is updated and what it outputs. Add the appropriate basic System object methods to set up and reset the object and set and validate the properties. Since this object supports nondirect feedthrough, you do not implement the stepImpl method. You implement the updateImpl and outputImpl 4-31

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methods instead. See the reference pages for each method and the full class definition file below for the implementation of each of these methods. • Use the setupImpl method to initialize some of the object’s properties. • Use the resetImpl method to reset the property states. • Use the validatePropertiesImpl method to check that the property values are valid. Add the following Nondirect mixin class methods instead of the stepImpl method to specify how the block updates its state and its output. See the reference pages and the full class definition file below for the implementation of each of these methods. • Use the outputImpl method to implement code to calculate the block output. • Use the updateImpl method to implement code to update the block’s internal states. • Use the isInputDirectFeedthroughImpl method to specify that the block is not direct feedthrough. Its inputs do not directly affect its outputs. Add the getIconImpl method to define the block icon when it is used in Simulink via the MATLAB System block. See the reference page and the full class definition file below for the implementation of this method. The full class definition file for the delay is: classdef intDelaySysObj < matlab.System &... matlab.system.mixin.Nondirect &... matlab.system.mixin.CustomIcon % intDelaySysObj Delay input by specified number of samples. % #codegen properties % InitialOutput Initial output InitialOutput = 0; end properties (Nontunable) % NumDelays Number of delays NumDelays = 1; end properties (DiscreteState) PreviousInput; end

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methods (Access = protected) function setupImpl(obj, ~) obj.PreviousInput = ones(1,obj.NumDelays)*obj.InitialOutput; end function [y] = outputImpl(obj, ~) % Output does not directly depend on input y = obj.PreviousInput(end); end function updateImpl(obj, u) obj.PreviousInput = [u obj.PreviousInput(1:end-1)]; end function flag = isInputDirectFeedthroughImpl(~,~) flag = false; end function validatePropertiesImpl(obj) if ((numel(obj.NumDelays)>1) || (obj.NumDelays 1) error('Initial output must be scalar value.'); end end function resetImpl(obj) obj.PreviousInput = ones(1,obj.NumDelays)*obj.InitialOutput; end function icon = getIconImpl(~) icon = sprintf('Integer\nDelay'); end end end

Test New System Objects in MATLAB 1

Create an instance of your new System object. For example, create an instance of the lmsSysObj. s = lmsSysObj;

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Run the object multiple times with different inputs. This tests for syntax errors and other possible issues before you add it to Simulink. For example, desired = 0; actual = 0.2; s(desired,actual);

Add System Objects to Your Simulink Model 1 2 3

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Add your System objects to your Simulink model by using the MATLAB System block as described in “Mapping System Objects to Block Dialog Box”. Add other Simulink blocks, connect them, and configure any needed parameters to complete your model as described in the Simulink documentation. See the System Identification for an FIR System Using MATLAB System Blocks Simulink example. Run your model in the same way you run any Simulink model.